${\bar{D}}_s^{(\ast )}{D}^{(\ast )}$ molecular state with $J^P=1^{+}$

Abstract

In this paper, we construct ${\bar{D}}_s^{(\ast )}{D}^{(\ast )}$-molecule-type interpolating currents $J_{(\pm )\mu }(x)$ with $J^P=1^{+}$, calculate the corresponding mass and magnetic moment using the QCD sum rule method and its extension in the weak electromagnetic field, and study the processes of $Z_{(\pm )cs}$ to ${\eta }_c{K}^{\ast }$, $J/\psi K$, $\bar{D}{D}_s^{\ast }$, and ${\bar{D}}^{\ast }{D}_s$ via three-point sum rules. The numerical values are $m_{Z_{(\pm )cs}}=3.99_{-0.14}^{+0.17}\text{mbox}GeV$, and ${\lambda }_{Z_{(\pm )cs}}=2.07_{-0.16}^{+0.28}\times 10^{-2}\text{mbox}{GeV}^5$, ${\mu }_{Z_{(\pm )cs}}=0.18_{-0.09}^{+0.16}{\mu }_N$ with ${\mu }_N$ the nucleon magneton, ${\Gamma }_{Z_{(+)cs}}=17.47_{-8.08}^{+12.70}$, and ${\Gamma }_{Z_{(-)cs}}=13.86_{-6.51}^{+10.37}$. The masses are in agreement with the recently measured value of $Z_{cs}(3985)$ by the BESIII Collaboration, $m_{Z_{cs}}^{exp}=(3982.5_{-2.6}^{+1.8}\pm 2.1)\text{mbox}MeV$. The widths are compatible with the experimental value, ${\Gamma }_{Z_{cs}}^{exp}=(12.8_{-4.4}^{+5.3}\pm 3.0)\text{mbox}MeV$. The magnetic moment and the various decay modes can help us to determine the inner structure of $Z_{cs}(3985)$ when being confronted with experimental data in the future.

Comments: 25 pages, 4 figures, published version